Tetrahedral packages have been manufactured and distributed for many years, and Tetra Pak® has been developing such systems since 1950. The normal tetrahedral package has a drawback, however, in that it not easily allows packaging in a space-convenient way. Specific odd-shaped secondary boxes were developed for handling the shipping, but they were costly and are not easily adapted to be packaged in automatic lines.
In US patent application from 1964, U.S. Pat. No. 3,347,363, an irregular tetrahedral package was disclosed which enabled tight packing within a cube. The general idea is that a cube can be filled completely by using a combination of irregular tetrahedrons and tetrahedrons with a mirrored shape thereof. An internet search of space-filling tetrahedrons reveals different possible packing patterns.
However, the irregular tetrahedrons are not easy to assemble into a cube since neither the intermediate or the final assembly is stable in itself. There is hence a need for additional support. In U.S. Pat. No. 3,347,363, it is mentioned that tetrahedral should be joined at their interfaces with some form of adhesive. It is also stated that a package comprised of a plurality of containers can include a rectangular three-dimensional enclosure (a box) for maintaining the containers in assembled condition. However, no details are mentioned for either the application of the adhesives of the enclosure for holding the packages assembled, or in what pattern the adhesive should be applied.
The general shape of the irregular tetrahedron, and its mirrored version, that can be used to completely fill a cube has been known at least since the year 1900. In reply to a problem posed by David Hilbert (the third Hilbert problem), Hilbert's student Max Dehn presented the proof in form of a counter-problem, inter alia comprising an irregular tetrahedron that, with a mirror version, completely could fill a cube. Guy Inchbald shows on his website www.steelpillow.com that you can use three irregular tetrahedrons and three mirrored versions for completely space filling a cube. This is also shown on the website www.korthalsaltes.com, which shows how four such tetrahedrons are assembled, lacking only a mirrored pair to complete the assembly. However, none of the latter mentions how six tetrahedrons can be held together in a box or similar assembly, in the tight cube packing pattern.